I spent the first 14 years of my career helping international students who were relocating to the United States. This involved helping them find their housing (often rentals) and also helping them to find services and adjust to a new country. For most of those years, my employment was with the University of California in a well-respected position focusing only on people relocating internationally, and I worked with people from 42 different countries.
I'd be happy to help you to find a place and to understand any of the differences in process that occur between countries. The other man who answered about the credit check is correct, but generally your visa application process will have required that you provide quite a bit of information financially before you get your visa. Much of that same documentation can be relevant and useful to prove your ability to be a good renter to owners of homes.
Are you coming here for work? ...or for a job? ...or for short-term stay? From your question, it sounded like you are probably moving here for a longer time. When will you be moving? What are your needs for a home? What is your budget? Where within the large city/area of Los Angeles are you moving? In addition to the concerns about international process, these basic concerns (which are true everywhere) can be the hurdles to overcome, and I can assist you with those (understanding neighborhoods and making sure you find the best home for you).
What part of Australia are you from? Large city or outlying areas?
When will you be moving here?
Rather than discussing your personal details in public, feel free to contact me directly at my contact information below. I'm more than happy to adjust my schedule to be appropriate for your timezone, and would love to assist you if I can.
Naia G. Waters
Realtor / Mentor of New Licensees
Prudential California Realty
3130 Wilshire Blvd., Suite 100
Santa Monica, CA 90403